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{"sheet":"README","index":0,"n_rows":173,"n_cols":16,"rows_kept":173,"cut":false,"hidden":false,"merged":[[2,6,2,11],[4,6,4,11],[6,6,6,11]]}
[]
[]
[null,null,null,null,null,null,"TONEARM  ALIGNMENT  WORKBOOK"]
[]
[null,null,null,null,null,null,"by Graeme Dennes"]
[]
[null,null,null,null,null,null,"2024-05-14"]
[]
[null,"Revision History"]
[null,null,"2021-09-24 Initial Release"]
[null,null,"2021-11-07 Correction to equalisation calculator"]
[null,null,"2022-03-22 Correction to the WTE derivative formula. My thanks to Peet Hickman."]
[null,null,"2022-05-28 The Derivatives setting of the Solver tool has been changed to Central (differencing) to provide improved accuracy for the \"perfect\" results. My thanks to Peet Hickman."]
[null,null,"2023-05-10 Minor overall improvements."]
[null,null,"2024-05-14    1. Added the 'Tests' sheet, titled Experimenter's Tonearm Alignment Workshop, for experimental and insight purposes. This is not an alignment-optimising sheet."]
[null,null,"                           It provides for arbitrary input values of the five fundamental parameters: R1, R2, L, β and d, and shows plots of the resulting tracking distortion, WTE and TE."]
[null,null,"                      2. The 'Perfect Löf C' sheet provides an option to lower the distortion at the inner or outer grooves, should this be required. Refer to the 'Perfect Löf C' sheet for details."]
[]
[null,"Introduction"]
[null,null,"This Excel workbook was created by the writer in 2008 but was not publicly released."]
[null,null,"Its fundamental purpose is to calculate the offset angle and overhang figures required to implement the tonearm alignment strategies and solutions from Löfgren (1938) and Stevenson (1966)."]
[null,null,"This workbook and the writer's accompanying tonearm alignment book were enhanced in 2010 to incorporate the four \"perfect\" alignment solutions, which utilise the enhanced accuracy capabilities of Excel's Solver tool."]
[null,null,"The first public release of this Excel workbook was in 2021 to accompany the 2021 release of the writer's tonearm alignment book."]
[]
[null,null,"Please note: This Excel workbook does not describe the strategies, techniques and calculations used by Löfgren and Stevenson to implement their alignment solutions."]
[null,null,"The writer's tonearm alignment book is the main reference for this Excel workbook."]
[null,null,"The latest releases of the tonearm alignment book and this Excel workbook may be downloaded from Vinyl Engine at:"]
[null,null,"https://www.vinylengine.com/turntable_forum/viewtopic.php?f=46&t=4854"]
[null,null,"The writer expresses his gratitude to JaS for hosting the files on Vinyl Engine."]
[]
[null,"Tonearm Alignments"]
[null,null,"This Excel workbook contains eight main alignment worksheets comprised of four 'perfect' sheets and four 'formula' sheets."]
[null,null,"The 'perfect' sheets are named 'Perfect Löf A', 'Perfect Löf B', 'Perfect Löf C' and 'Perfect Stev A'. These use the Excel Solver tool to provide the maximum possible accuracy for the calculated alignment figures."]
[null,null,"The 'formula' sheets are named 'Löf A', 'Löf B', 'Löf C' and 'Stev A'. These use the alignment formulas presented by their respective authors."]
[null,null,"This Excel workbook requires the use of the Solver tool. To install the Solver tool, refer below."]
[]
[null,null,"A sheet named 'Perfect Löf C Trap' is included. It uses a worksheet-based composite trapezoidal rule numerical integrator and RMS distortion calculator to also calculate the 'perfect' offset angle and overhang"]
[null,null,"figures for the 'Löfgren C' alignment. Although not as accurate as the 'Perfect Löf C' sheet (which uses a separate RMS distortion calculator, described below), it is included here for reference to the trapezoidal rule"]
[null,null,"'Perfect Löfgren C' worksheet calculator described in the writer's tonearm alignment book."]
[]
[null,null,"A sheet named 'Löf EQN (46)' is included for historical and reference purposes to demonstrate the calculation of the mean and RMS distortion using Löfgren's EQN (46)."]
[null,null,"Although the least accurate of the three distortion calculators provided in this workbook, the EQN (46) distortion formula is fully described in the writer's tonearm alignment book."]
[]
[null,null,"The sheet named 'Tests' is included to enable experimentation with the five key alignment parameters: R1, R2, L, β and d and to observe their effects on the tracking distortion, WTE and TE by way of plots."]
[null,null,"Please note: The 'TESTS' sheet is not an alignment-optimising sheet."]
[]
[null,"High-Accuracy WTE Formula"]
[null,null,"All WTE calculations in this workbook use Löfgren's high-accuracy, no-approximation WTE formula: WTE = TAN(tracking error) / radius."]
[null,null,"The 2021 release of the writer's tonearm alignment book was revised to include this high-accuracy WTE formula."]
[null,null,"It replaces the small angle approximations (SAAs) formula used in Löfgren's EQN (22) and as was used in previous releases of this workbook (WTE = tracking error (radians) / radius)."]
[]
[null,"This Excel workbook contains 13 worksheets. The instructions for using the eight main alignment worksheets are provided on the worksheets."]
[]
[null,null,"1.     This 'Readme' sheet."]
[]
[null,null,"2.     'Löf A' sheet, Löfgren's prime alignment strategy, 'Löfgren A'. Uses Löfgren's formulas. Calculates the optimum offset angle and overhang which minimises and equalises the magnitudes"]
[null,null,"        of the three WTE peaks."]
[]
[null,null,"3.     'Perfect Löf A' sheet, the 'Löfgren A' alignment calculated using the Excel Solver tool to provide the highest possible accuracy for the offset angle and overhang required."]
[]
[null,null,"4.     'Löf B' sheet, Löfgren's compromise alignment strategy, 'Löfgren B'. Uses Löfgren's formulas. Calculates the optimum overhang which minimises the RMS distortion for situations"]
[null,null,"        where the offset angle is fixed and non-optimum."]
[]
[null,null,"5.     'Perfect Löf B' sheet, the 'Löfgren B' alignment calculated using the Excel Solver tool to provide the highest possible accuracy for the overhang required."]
[]
[null,null,"6.     'Löf C' sheet, Löfgren's alternative alignment strategy, 'Löfgren C'. Uses the linear offset formula by Vladan Jovanovic and Löfgren's 'Löfgren B' overhang formula. Löfgren did not provide a solution"]
[null,null,"        for this alignment. Calculates the optimum offset angle and overhang which minimises the RMS distortion as the means to reduce the magnitude of the central WTE peak of the 'Löfgren A' alignment"]
[null,null,"        for situations where the magnitude may be considered objectionable, given that the WTE and distortion change only slowly in this area of the record playing surface."]
[]
[null,null,"7.     'Perfect Löf C' sheet, the 'Löfgren C' alignment calculated using the Excel Solver tool to provide the highest possible accuracy of the offset angle and overhang required."]
[]
[null,null,"8.     'Stev A' sheet, Stevenson's prime alignment strategy, 'Stevenson A'. Based on Stevenson's and Löfgren's formulas. Calculates the optimum offset angle and overhang which sets the WTE at the inner groove to zero."]
[]
[null,null,"9.     'Perfect Stev A' sheet, the 'Stevenson A' alignment calculated using the Excel Solver tool to provide the highest possible accuracy of the offset angle and overhang required."]
[]
[null,null,"10.    'Perfect Löf C Trap' sheet, an optional (but less accurate) 'perfect Löf C' alignment calculated using the Trapezoidal Rule integrator as described in the writer's tonearm alignment book (for reference purposes only)."]
[]
[null,null,"11.    'Löf Eqn (46)' sheet, an optional distortion calculator based on Löfgren's EQN (46) as described in the writer's tonearm alignment book. (For historical and reference purposes only.)"]
[]
[null,null,"12.   'Tests' sheet, provided to show graphs of tracking distortion, WTE and TE when the five key alignment parameters: R1, R2, L, β and d are manually selected to assist with experimental or what-if alignment situations."]
[]
[null,null,"13.    'Plots' sheet, showing the plots of tracking distortion and WTE between the groove radii R1 and R2 for the eight main alignment sheets. Provides adjustable recording parameters and equalisation options."]
[null,null,"         Of great interest is the degree the four \"formula\" plots match the respective four \"perfect' plots."]
[]
[null,"Symbols used in this workbook"]
[null,null,"WTE","Weighted tracking error at radius R, TAN(TE) per mm"]
[null,null,"TA","Tracking angle at radius R in degrees"]
[null,null,"TE","Tracking error at radius R in degrees"]
[null,null,"R1","Inner groove radius in mm"]
[null,null,"R2","Outer groove radius in mm"]
[null,null,"L","Tonearm length in mm"]
[null,null,"β","Offset angle in degrees"]
[null,null,"d","Overhang in mm"]
[null,null,"R01","Inner zero (null) radius in mm"]
[null,null,"R02","Outer zero (null) radius in mm"]
[null,null,"p","Linear offset in mm"]
[null,null,"M","Mounting distance in mm"]
[null,null,"Rw","Radius in mm at the minimum of the weighted tracking error curve"]
[null,null,"Ra","Radius in mm at the minimum of the angular tracking error curve"]
[null,null,"%RMS Tracking Distortion",null,"The %RMS second harmonic distortion of a 1 KHz tone due to WTE. The RIAA roll-off is included."]
[]
[null,"Universal (Alignment-Independent) Formulas"]
[null,null,"These Excel formulas are independent of the alignment method and may be universally applied."]
[null,null,"The formulas are exact, except where noted."]
[null,null,"Note that Excel's angular mode is radians."]
[null,null,"WTE = TAN ( ASIN ( ( R2 + L2 - M2 ) / ( 2 * L * R ) ) -  β * PI  / 180 ) / R"]
[null,null,"TA = ASIN(( R2 + L2 – M2 ) / ( 2 * L * R )) * 180 / PI"]
[null,null,"TE = TA – β"]
[null,null,"M = L – d"]
[null,null,"M = SQRT ( L2 – Ra2 )"]
[null,null,"d = L – SQRT ( L2 – Ra2 )"]
[null,null,"L2 – M2 = 2 * L * d – d2"]
[null,null,"Ra2 = L2 – M2"]
[null,null,"Ra2 =  2 * L * d – d2"]
[null,null,"Ra2 = R01 * R02"]
[null,null,"Rw = Ra2 / p         <<< Uses small angle approximations. For maximum accuracy, use the Solver tool to find Rw as is done for the \"perfect\" sheets."]
[null,null,"p = L * sin β"]
[null,null,"p = ( R01 + R02 ) / 2"]
[null,null,"R01 = p –SQRT ( p2 – Ra2 )"]
[null,null,"R02 = p + SQRT ( p2 – Ra2 )"]
[]
[null,"RMS Distortion Calculator"]
[null,null,"Most worksheets call the RMS distortion program to calculate and display the RMS distortion figures shown on the worksheets."]
[null,null,"The program is located in the VBA module m_RMS_DISTORTION."]
[null,null,"The RMS distortion figures represent the level of second harmonic distortion caused by WTE for a 1 KHz tone with a maximum peak recorded velocity of 100 mm/sec and a turntable speed of 33 1/3 RPM."]
[null,null,"These constants are stored in the RMS distortion program. RIAA playback de-emphasis is included in the RMS distortion calculations."]
[null,null,"In this application, the RMS distortion results are usually accurate to the 15 significant digits displayed because of the exceptional accuracy of the RMS Distortion program and the smoothness of the WTE function."]
[]
[null,null,"The RMS distortion program is called with five parameters in the order of: (1) radius R1 in mm, (2) radius R2 in mm, (3) arm length L in mm, (4) offset angle β in degrees, (5) overhang d in mm."]
[null,null,"As an example of calling with numeric values, the cell formula is of the form:  =RMS_DISTORTION(60.325, 146.05, 250, 22, 16)."]
[null,null,"As an example of calling with cell references, the cell formula is of the form:  =RMS_DISTORTION(A1, B2, C3, D4, E5)."]
[null,null,"Multiply the result by 100 for %RMS distortion."]
[]
[null,"Playback Equalisation Calculator"]
[null,null,"The workbook includes a VBA-coded playback equalisation calculator which is used by the 'Plots' sheet. The function name is EQUALISATION."]
[null,null,"It allows for the selection of the RIAA response, the IEC response or a flat (no EQ) response, and can provide its result as a gain figure or a decibel figure."]
[null,null,"It may also be called as a function by other programs for providing equalisation calculations."]
[null,null,"A complete explanation of the purpose, use and examples for using it are included at the beginning of the code in the VBA module m_EQUALISATION, so is not repeated here."]
[]
[null,"Quick Calculator Box"]
[null,null,"The alignment worksheets include a Quick Calculator box to calculate the WTE, tracking angle, tracking error and tracking distortion for the entered radius."]
[null,null,"The tracking distortion is based on a fundamental frequency of 1 KHz with RIAA correction."]
[]
[null,"Unintentional Data Entry Protection for Worksheets"]
[null,null,"For safety, all worksheets except the 'Plots' sheet are protected from unintentional (destructive) data entry via Excel's data validation rules. Only the worksheet data input cells allow entry of data."]
[null,null,"However, part of or all such protection may be readily removed via the data validation settings under Data tab / Data Tools group / Data Validation (small red circle)."]
[null,null,"To protect a cell, range of cells or a worksheet against data entry, select the cell(s) then select Data tab / Data Tools group / Data Validation / Settings / Validation Criteria / Allow Text Length / Equal to / 0, then OK."]
[null,null,"To remove the protection from a cell, range of cells or a worksheet, select the cell(s) then select Data tab / Data Tools group / Data Validation / Settings / Clear All, then OK."]
[]
[null,"Adding the Solver Tool in Excel"]
[null,null,"The Excel Solver Add-in is a Microsoft Office add-in tool that is included when Excel is installed. It is not usually enabled by default. This workbook requires the Solver tool."]
[null,null,"Firstly, the Solver tool needs to be enabled in Excel as follows:"]
[null,null,"1. Open Excel."]
[null,null,"2. In Excel 2010 and later, go to File > Options"]
[null,null,"    In Excel 2007, click the Microsoft Office Button and then click Excel Options."]
[null,null,"3. On the left menu list, click Add-Ins, and then in the Manage box, select Excel Add-ins."]
[null,null,"4. Click Go."]
[null,null,"5. In the Add-Ins available box, click the Solver Add-in check box and then click OK."]
[null,null,"6. After the Solver Add-in is enabled, the Solver command is available in the Analysis group on the Data tab."]
[]
[null,null,"Secondly, the Solver tool needs to be added to the Visual Basic References as follows:"]
[null,null,"1. In Excel, click the Developer tab. (If not showing, the Developer option must be added separately)."]
[null,null,"2. Click the Visual Basic option in the Code group."]
[null,null,"3. In the VBA window, click the Tools option, then click References…"]
[null,null,"4. Locate the Solver entry in the available References list then check the box alongside it."]
[null,null,"5. Click OK to close the References window, then close the VBA window."]
[]
[null,"Copyright © 2008, 2024  Graeme Dennes"]
[null,null,"1. This Excel workbook is free software: you may redistribute it and/or",null,null,null,null,null,null,"2. This program is distributed in the hope that it will be useful,",null,null,null,null,null,"3. See the GNU General Public License (GGPL) for more details."]
[null,null,"    modify it under the terms of the GNU General Public License as",null,null,null,null,null,null,"    but WITHOUT ANY WARRANTY; without even the implied warranty of",null,null,null,null,null,"    A copy of the GNU General Public License is available at"]
[null,null,"    published by the Free Software Foundation, either version 3 of the",null,null,null,null,null,null,"    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.",null,null,null,null,null,"    http://www.gnu.org/licenses/gpl-3.0.html"]
[null,null,"    License, or (at your option) any later version, as long as this copyright",null,null,null,null,null,null,"    See the GNU General Public License (GGPL) for more details."]
[null,null,"    notice is included in full."]

{"sheet":"LÖF A","index":1,"n_rows":45,"n_cols":8,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove radius R1 =  ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'LÖFGREN A' CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING LÖFGREN'S EQUATIONS",null,60.325000000000003]
[]
[null,"OUTPUT","Offset angle β = ",{"$f":"DEGREES(ASIN(($D$2*$D$3*($D$2+$D$3))/$D$4/(($D$2+$D$3)^2/4+$D$2*$D$3)))","v":21.94887040000955}," degrees",null,null,"WTE: TAN(TE) per mm"]
[null,"OUTPUT","Overhang d = ",{"$f":"$D$4-SQRT($D$4^2-$D$13)","v":16.50182274811911}," mm","INSTRUCTIONS",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.0411430801616756E-4}]
[null,null,null,null,null,"1. Enter R1 into D2, R2 into D3, L into D4.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",{"$f":"(2*$D$2*$D$3)/($D$2+$D$3)","v":85.383076923076942}," mm","2. The optimum offset angle β is shown in D6,",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":22.654328890784246}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":7.5286038579567374E-9}," TAN(TE) per mm2","    and the optimum overhang d is shown in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":89.323016183116081}," mm","3. The %RMS tracking distortion is shown in D27.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":0.70545849077469569}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":1.9527646786006848E-18}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"(2*($D$2*$D$3)^2)/(($D$2+$D$3)^2/4+$D$2*$D$3)","v":7978.6012200492178}," mm2",null,null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.43404928017498989}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":65.998046374175644}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":120.89147570845616}," mm",null,null,"Löfgren's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$6*PI()/180)","v":0.37377904416526359},null,null,null,"Minimise and equalise the magnitudes of"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":93.4447610413159}," mm",null,null,"the three weighted tracking error peaks."]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":233.49817725188089}," mm"]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":2.0411430801616756E-4}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-2.0291471347774333E-4}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.0491910748948687E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.43404928017498989}," (Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.43149834118905839}," (Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.43576068706005638}," (Includes RIAA term)"]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":-8.0479947331930728E-7}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R1 + WTE at RW =  ",{"$f":"$D$19+$D$20","v":1.1995945384242295E-6}," TAN(TE) per mm"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$6,$D$7)*100","v":0.28763789604552326}," (Includes RIAA term)"]
[]
[]
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[]
[null,null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"LÖF A"}]

{"sheet":"PERFECT LÖF A","index":2,"n_rows":43,"n_cols":8,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'PERFECT  LÖFGREN A'  CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING  THE  SOLVER  TOOL",null,146.05000000000001]
[]
[null,"INPUT/OUTPUT","Offset angle β = ",21.962997305126706," degrees","INSTRUCTIONS",null,"WTE: TAN(TE) per mm"]
[null,"INPUT/OUTPUT","Overhang d = ",16.515729704977336," mm","1. Enter R1 into D2, R2 into D3, L into D4.",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.0389482974961793E-4}]
[null,null,null,null,null,"2. Click the orange button to run the Solver.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",85.388512135642401," mm","3. The \"perfect\" offset angle β is shown in D6 and",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":23.668695076007904}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":3.6253010142484055E-19}," TAN(TE) per mm2","    the \"perfect\" overhang d is shown in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":89.359361707662146}," mm","4. The %RMS tracking distortion is shown in D27.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":1.7056977708811978}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"$D$4^2-$D$18^2","v":7985.0955248007958}," mm2","%RMS Tracking Distortion Calculator",null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.4335825594216246}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":65.978931035100231}," mm","1. Enter arm length L in D4, offset angle β in D6 and overhang d in D7."]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":121.02493022435894}," mm","2. Read the resulting %RMS tracking distortion in D27.",null,"Löfgren's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$6*PI()/180)","v":0.37400772251891834},null,null,null,"Minimise and equalise the magnitudes of"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":93.501930629729586}," mm","SOLVER SETTINGS",null,"the three weighted tracking error peaks."]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":233.48427029502267}," mm","Objective Cell =  D25 (WTE R1 - WTE R2)         Equal to Value of: 0"]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":2.0389482974961744E-4}," TAN(TE) per mm","Changing Cells = D6 (β), D7 (d), D9 (Rw)"]
[null,"OPTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-2.0389482974961603E-4}," TAN(TE) per mm","Constraints: D10 = 0 (Derivative of WTE function = 0 at Rw)"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.0389482974961793E-4}," TAN(TE) per mm","                   D26 = 0 (WTE R1 + WTE Rw = 0)"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.4335825594216236},"(Includes RIAA term)","Make Unconstrained Variables Non-Negative."]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.43358255942162066},"(Includes RIAA term)","Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.4335825594216246},"(Includes RIAA term)","Use Automatic Scaling.     Max Time: 100 seconds."]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":-4.87890977618477E-19}," TAN(TE) per mm","Iterations: 10000.     Convergence: 1E-14     Derivatives: Central."]
[null,"OUTPUT","WTE at R1 + WTE at RW =  ",{"$f":"$D$19+$D$20","v":1.4094628242311558E-18}," TAN(TE) per mm","Require Bounds on Variables."]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$6,$D$7)*100","v":0.2883982950684244},"(Includes RIAA term)"]
[]
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[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"PERFECT LÖF A"}]

{"sheet":"LÖF B","index":3,"n_rows":45,"n_cols":8,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'LÖFGREN B' CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING LÖFGREN'S EQUATIONS",null,146.05000000000001]
[null,"INPUT","Offset angle β = ",21," degrees"]
[null,null,null,null,null,null,null,"WTE: TAN(TE) per mm"]
[null,"OUTPUT","Overhang d = ",{"$f":"$D$4-SQRT($D$4^2-$D$13)","v":15.635807533403693}," mm","INSTRUCTIONS",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$5*PI()/180)/$H$4","v":2.7697813238910737E-4}]
[null,null,null,null,null,"1. Enter R1 into D2, R2 into D3, L into D4.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",{"$f":"$D$13/$D$17","v":84.53239525565175}," mm","2. Enter offset angle β into D5.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":23.316503434474111}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$5*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$5*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":2.953277991272956E-9},"TAN(TE) per mm2","3. The optimum overhang d is shown in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":87.025428981879756}," mm","4. The %RMS tracking distortion is shown in D27.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$5)","v":2.3165034344741109}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":-2.0496351524694054E-18},"TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"3*$D$2*$D$3*($D$17*($D$2+$D$3)-$D$2*$D$3)/(($D$2+$D$3)^2-$D$2*$D$3)","v":7573.4252894801975}," mm2",null,null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.58899427559082485}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":68.301169779872453}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":110.88280499277769}," mm",null,null,"Löfgren's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$5*PI()/180)","v":0.35836794954530027},null,null,null,"A compromise alignment which minimises"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":89.591987386325073}," mm",null,null,"the RMS distortion for when the offset angle"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":234.36419246659631}," mm",null,null," is fixed and non-optimum."]
[null,"OUTPUT","WTE at R1 =",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$5*PI()/180)/$D$2","v":2.3807275359898633E-4}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at RW =",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$5*PI()/180)/$D$9","v":-1.2796620329238762E-4}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R2 =",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$5*PI()/180)/$D$3","v":2.7697813238910737E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.50626194867599739},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.27212025930777839},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.58899427559082485},"(Includes RIAA term)"]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":-3.8905378790121036E-5}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R1 + WTE at RW = ",{"$f":"$D$19+$D$20","v":1.1010655030659872E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$5,$D$7)*100","v":0.26986885776349484},"(Includes RIAA term)"]
[]
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[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"LÖF B"}]

{"sheet":"PERFECT LÖF B","index":4,"n_rows":43,"n_cols":8,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'PERFECT  LÖFGREN B'  CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING  THE  SOLVER  TOOL",null,146.05000000000001]
[null,"INPUT","Fixed offset angle β = ",21," degrees"]
[null,null,null,null,null,"INSTRUCTIONS",null,"WTE: TAN(TE) per mm"]
[null,"INPUT/OUTPUT","Overhang d = ",15.630380319935378," mm","1. Enter R1 into D2, R2 into D3, L into D4.",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$5*PI()/180)/$H$4","v":2.7671797507681486E-4}]
[null,null,null,null,null,"2. Enter the fixed, non-optimum offset angle β into D5.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",84.499286583121247," mm","3. Click the orange button to run the Solver.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":23.314329978782816}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$5*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$5*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":5.3571098498537105E-15}," TAN(TE) per mm2","4. Read the \"perfect\" overhang d in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":87.010811805326014}," mm","5. The %RMS tracking distortion is shown in D27.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$5)","v":2.3143299787828155}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"$D$4^2-$D$18^2","v":7570.8813710218601}," mm2","%RMS Tracking Distortion Calculator",null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.58844105080599551}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":68.241511213425071}," mm","1. Enter arm length L in D4, offset angle β in D5 and overhang d in D7."]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":110.94246355922508}," mm","2. Read the resulting %RMS tracking distortion in D27.",null,"Löfgren's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$5*PI()/180)","v":0.35836794954530027},null,null,null,"A compromise alignment which minimises"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":89.591987386325073}," mm","SOLVER SETTINGS",null,"the RMS distortion for when the offset angle"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":234.36961968006463}," mm","Objective Cell: D27 (%RMS Tracking Distortion)       Equal to:  Minimum",null," is fixed and non-optimum."]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$5*PI()/180)/$D$2","v":2.3656644643665114E-4}," TAN(TE) per mm","Changing Cells: D7 (d), D9 (Rw)"]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$5*PI()/180)/$D$9","v":-1.2872618865280503E-4}," TAN(TE) per mm","Constraint: D10 = 0 (Derivative of WTE function = 0 at Rw)"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$5*PI()/180)/$D$3","v":2.7671797507681486E-4}," TAN(TE) per mm","Make Unconstrained Variables Non-Negative."]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.50305878498850998},"(Includes RIAA term)","Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.27373636893693082},"(Includes RIAA term)","Use Automatic Scaling.     Max Time: 100 seconds."]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.58844105080599551},"(Includes RIAA term)","Iterations: 10000.     Convergence: 1E-14     Derivatives: Central."]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":-4.0151528640163724E-5}," TAN(TE) per mm","Require Bounds on Variables."]
[null,"OUTPUT","WTE at R1 + WTE at RW = ",{"$f":"$D$19+$D$20","v":1.0784025778384611E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$5,$D$7)*100","v":0.26986475937379473},"(Includes RIAA term)"]
[]
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[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"PERFECT LÖF B"}]

{"sheet":"LÖF C","index":5,"n_rows":45,"n_cols":8,"rows_kept":45,"cut":false,"hidden":false,"merged":[[21,5,21,6],[24,5,24,6],[25,5,25,6]]}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'LÖFGREN C' CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING LÖFGREN'S AND JOVANOVIC'S EQUATIONS",null,146.05000000000001]
[]
[null,"OUTPUT","Offset angle β = ",{"$f":"DEGREES(ASIN($D$17/$D$4))","v":21.82842702035023}," degrees",null,null,"WTE: TAN(TE) per mm"]
[null,"OUTPUT","Overhang d = ",{"$f":"$D$4-SQRT($D$4^2-$D$13)","v":16.797987974032509}," mm","INSTRUCTIONS",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.3349757236051187E-4}]
[null,null,null,null,null,"1. Enter R1 into D2, R2 into D3, L into D4.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",{"$f":"$D$13/$D$17","v":87.317917821908836}," mm","2. The optimum offset angle β is shown in  D6,",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":23.781589132840136}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":3.6076406145815162E-9}," TAN(TE) per mm2","    and the optimum overhang d in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":90.093404792140632}," mm","3. The %RMS tracking distortion is shown in D27.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":1.9531621124899061}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"(3*$D$2*$D$3*($D$17*($D$2+$D$3)-$D$2*$D$3))/($D$2^2+$D$2*$D$3+$D$3^2)","v":8116.8215870405083}," mm2",null,null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.49653282119575892}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":70.061626033285052}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":115.85260072588594}," mm","EQUATION-BASED 'LÖFGREN C' ALIGNMENT",null,"Löfgren's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"$D$17/$D$4","v":0.37182845351834198},null,"This is an historic first!",null,"An alternative alignment to address possible"]
[null,"OUTPUT","Linear offset p = ",{"$f":"2*($D$2*$D$3*(2*($D$2^2+$D$2*$D$3+$D$3^2)*LN($D$3/$D$2)-3*($D$3^2-$D$2^2))/($D$3-$D$2)^3)/((1+$D$2*$D$3/$D$4^2)+SQRT((1+$D$2*$D$3/$D$4^2)^2-4*($D$2*$D$3*(2*($D$2^2+$D$2*$D$3+$D$3^2)*LN($D$3/$D$2)-3*($D$3^2-$D$2^2))/($D$3-$D$2)^3)^2/$D$4^2))","v":92.957113379585493}," mm","This alignment is made possible by the development of an equation",null,"objections to the magnitude of the central WTE"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":233.20201202596749}," mm","for the linear offset p by Vladan Jovanovic in 2021, from which",null,"peak of the 'Löfgren A' alignment."]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":3.2139176997800765E-4}," TAN(TE) per mm","the offset angle is calculated. Although Löfgren provided"]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-1.3881414092910266E-4}," TAN(TE) per mm","a solution for the overhang for the Löfgren C alignment,"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.3349757236051187E-4}," TAN(TE) per mm","a solution for the offset angle was not given. We now have it!"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.68343992035125045},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.29518840954360798},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.49653282119575892},"(Includes RIAA term)"]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":8.7894197617495782E-5}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R1 + WTE at RW = ",{"$f":"$D$19+$D$20","v":1.8257762904890499E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$6,$D$7)*100","v":0.25840076443186377},"(Includes RIAA term)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"LÖF C"}]

{"sheet":"PERFECT LÖF C","index":6,"n_rows":43,"n_cols":12,"rows_kept":43,"cut":false,"hidden":false,"merged":[[21,9,21,11],[22,9,22,11],[20,9,20,11],[26,9,26,11],[17,9,17,11],[18,9,18,11],[23,9,23,11],[24,9,24,11],[25,9,25,11],[19,9,19,11],[7,9,7,11],[8,9,8,11],[14,9,14,11],[15,9,15,11],[16,9,16,11],[12,9,12,11],[13,9,13,11],[10,9,10,11],[11,9,11,11]]}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'PERFECT  LÖFGREN C'  CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING  THE  SOLVER  TOOL",null,146.05000000000001]
[]
[null,"INPUT/OUTPUT","Offset angle β = ",21.840515421669771," degrees","INSTRUCTIONS",null,"WTE: TAN(TE) per mm",null,"INPUT","Q = ",0]
[null,"INPUT/OUTPUT","Overhang d = ",16.809133710271144," mm","1. Enter R1 into D2, R2 into D3, L into D4.",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.3258456291678982E-4}]
[null,null,null,null,null,"2. Enter Q into L6 (upper right).",null,"Tracking Angle (degrees)",null,"If Q = 0, the 'PERFECT LÖF C'"]
[null,"OUTPUT","Radius Rw = ",87.32173703480872," mm","3. Click the orange button to run the Solver.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":23.786046267028681},null,"alignment solution is provided."]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":-4.5686839592528825E-18}," TAN(TE) per mm2","4. Read the \"perfect\" offset angle β in D6.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":90.122249633738036}," mm","5. Read the \"perfect\" overhang d in D7.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":1.9455308453589097},null,"OPTIONAL SOLUTION"]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm","6. The %RMS tracking distortion is shown in D27.",null,"%Tracking Distortion (includes RIAA term)",null,"As an option to lower the tracking"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"$D$4^2-$D$18^2","v":8122.0198790457944}," mm2",null,null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.4945913057003869},null,"distortion at the inner or outer groove"]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":70.025428231494089}," mm","%RMS Tracking Distortion Calculator",null,null,null,"areas to favour the playback of particular"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":115.98672202611249}," mm","1. Enter arm length L in D4, offset angle β in D6 and overhang d in D7.",null,"Löfgren's Alignment Strategy:",null,"tracks, the Q factor is provided."]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$6*PI()/180)","v":0.37202430051521318},null,"2. Read the resulting %RMS tracking distortion in D27.",null,"Löfgren's alternative alignment to address possible",null,"If Q > 0, the tracking distortion at R1 is"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":93.006075128803289}," mm",null,null,"objections to the magnitude of the central WTE",null,"set to Q times the tracking distortion at"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":233.19086628972886}," mm","SOLVER SETTINGS",null,"peak of the 'Löfgren A' alignment.",null,"R2. This means that for 0 < Q < 1, the"]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+$D$4^2-$D$18^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":3.2099654833490086E-4}," TAN(TE) per mm","Objective Cell: D27 (%RMS Tracking Distortion)       Equal to:  Minimum",null,null,null,"tracking distortion at the inner grooves"]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+$D$4^2-$D$18^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-1.3976858669612053E-4}," TAN(TE) per mm","Changing Cells:   D6 (β), D7 (d), D9 (Rw)",null,null,null,"is lowered; for Q > 1, the tracking"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+$D$4^2-$D$18^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.3258456291678944E-4}," TAN(TE) per mm","Constraint: D10 = 0    (Derivative of WTE function = 0 at Rw)",null,null,null,"distortion at the outer grooves is lowered,"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.68259948113183755},"(Includes RIAA term)","Optional constraint: If Q > 0, D19 = Q x D21",null,null,null,"and for Q = 1, the tracking distortions at"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.29721803942191793},"(Includes RIAA term)","Make Unconstrained Variables Non-Negative.",null,null,null,"R1 and R2 are made equal."]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.49459130570038612},"(Includes RIAA term)","Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14",null,null,null,"(The RMS distortion remains minimised.)"]
[null,"OUTPUT","WTE at R1 - WTE at R2 = ",{"$f":"$D$19-$D$21","v":8.8411985418111413E-5}," TAN(TE) per mm","Use Automatic Scaling.     Max Time: 100 seconds.",null,null,null,"Refer to the 'PERFECT LÖF C' plots on"]
[null,"OUTPUT","WTE at R1 + WTE at RW = ",{"$f":"$D$19+$D$20","v":1.8122796163878033E-4}," TAN(TE) per mm","Iterations: 10000.     Convergence: 1E-14     Derivatives: Central.",null,null,null,"the PLOTS sheet to observe the effects"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2, $D$3, $D$4, $D$6,$D$7)*100","v":0.25839343844324597},"(Includes RIAA term)","Require Bounds on Variables.",null,null,null,"of Q on tracking distortion and WTE."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"PERFECT LÖF C"}]

{"sheet":"PERFECT LÖF C TRAP","index":7,"n_rows":17175,"n_cols":11,"rows_kept":4500,"cut":true,"hidden":false,"merged":[[1,5,1,7],[2,5,2,7],[3,5,3,7],[14,9,14,10],[4,5,4,7],[7,5,7,7],[12,5,12,7],[5,5,5,7],[6,5,6,7],[10,5,10,7],[15,9,15,10],[8,5,8,7],[25,5,25,7],[14,5,14,7],[24,5,24,7],[23,5,23,7],[11,5,11,7],[15,5,15,7],[16,5,16,7],[19,5,19,7],[17,5,17,7],[18,5,18,7],[20,5,20,7],[21,5,21,7],[22,5,22,7]],"bounds":{"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0}}
[]
[null,"INPUT","Inner groove radius R1 = ",60.325000000000003," mm",null,null,null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius  R2 = ",146.05000000000001," mm","'PERFECT  LÖFGREN C'  CALCULATOR  USING  THE  SOLVER  TOOL",null,null,null,"Enter Radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","AND  WORKSHEET  TRAPEZOIDAL  RULE  INTEGRATOR",null,null,null,146.05000000000001]
[null,null,null,null,null,"INSTRUCTIONS"]
[null,"INPUT/OUTPUT","Offset angle β = ",21.84051536116117," degrees","1. Enter R1 into D2, R2 into D3 and L into D4.",null,null,null,"WTE: TAN(TE) per mm"]
[null,"INPUT/OUTPUT","Overhang d = ",16.809133598645268," mm","2. Click the orange button (may take several seconds).",null,null,null,{"$f":"TAN(ASIN(($J$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$J$4))-$D$6*PI()/180)/$J$4","v":2.3258456481549796E-4}]
[null,null,null,null,null,"3. Read the \"perfect\" offset angle β in D6, the \"perfect\" Overhang d",null,null,null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",87.321736698927239," mm","    in D7 and the %RMS tracking distortion in D25.",null,null,null,{"$f":"((DEGREES(ASIN((($J$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$J$4)))))","v":23.786046222390251}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":-3.6541420625859408E-15}," TAN(TE) per mm2",null,null,null,null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":90.122249344906677}," mm","%RMS Tracking Distortion Calculator",null,null,null,{"$f":"((DEGREES(ASIN((($J$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$J$4))))-$D$6)","v":1.9455308612290807}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm","1. Enter arm length L in D4, offset angle β in D6 and overhang d in D7.",null,null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"$D$4^2-$D$18^2","v":8122.0198269855318}," mm2","2. Read the resulting %RMS tracking distortion in D25.",null,null,null,{"$f":"ABS($J$7)*90/PI()*0.742288880049004*100","v":0.49459130973799165}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$2,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13)))","v":70.025427845554887}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":115.98672192191547}," mm","SOLVER SETTINGS",null,null,null,"The figures shown below form the calculation sequence based on"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$6*PI()/180)","v":0.37202429953494071},null,"Objective Cell: D25 (%RMS Tracking Distortion)       Equal to:  Minimum",null,null,null,"the values showing in cells D2, D3, D4, D6 and D7."]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":93.006074883735181}," mm","Changing Cells:  D6 (β), D7 (d), D9 (Rw)",null,null,null,"Sum of Totals = ",{"$f":"SUM(J30:J17175)","v":0.41551294986796694}]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":233.19086640135473}," mm","Constraint: D10 = 0 (Derivative of WTE function = 0 at Rw)",null,null,null,"Radius interval = ",{"$f":"$D$3-$D$2","v":85.725000000000009}]
[null,"OUTPUT","WTE at R1 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":3.209965347652799E-4}," TAN(TE) per mm","Make Unconstrained Variables Non-Negative.",null,null,null,"No. of  radius panels = ",{"$f":"17146-1","v":17145}]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-1.3976858924282505E-4}," TAN(TE) per mm","Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14",null,null,null,"Integral = ",{"$f":"$K$17*$K$18/(2*$K$19)","v":1.0387823746699175E-3}]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.3258456481549796E-4}," TAN(TE) per mm","Use Automatic Scaling.     Max Time: 100 seconds.",null,null,null,"Mean distortion method 1 = ",{"$f":"$K$20/$K$18","v":1.2117613002857013E-5}]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":0.68259945227602503},"(Includes RIAA term)","Iterations: 10000.     Convergence: 1E-14     Derivatives: Central.",null,null,null,"Mean distortion method 2 = ",{"$f":"$K$17/(2*$K$19)","v":1.2117613002857011E-5}]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.29721804483748765},"(Includes RIAA term)","Require Bounds on Variables.",null,null,null,"RMS distortion = ",{"$f":"SQRT($K$21)","v":3.4810361967174391E-3}]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.49459130973799165},"(Includes RIAA term)","This sheet is included as a reference to the Trapezoidal Rule",null,null,null,"RMS dist. with RIAA term = ",{"$f":"$K$23*0.742288880049004","v":2.5839344598714321E-3}]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"SQRT(SUM($J$30:$J$17175)/34290)*0.742288880049004*100","v":0.25839344598714314},"(Includes RIAA term)","'perfect Löfgren C' calculator presented in Section 1 of the writer's",null,null,null,"%RMS distortion = ",{"$f":"$K$24*100","v":0.2583934459871432}]
[null,null,null,null,null,"tonearm alignment book. Not as accurate as the 'PERFECT LÖF C' sheet."]
[]
[null,1,2,3,4,5,6,7,8,9]
[null,"Line No.","Radius (mm)","Tracking Angle (Degrees)","Tracking Error (Degrees)","WTE (TAN(TE) per mm)","Distortion Parameter, K","Distortion Parameter Squared, K^2","Multiplier","Total"]
[null,1,60.325000000000003,{"$f":"DEGREES(ASIN((C30^2+2*$D$4*$D$7 -$D$7^2)/(2*$D$4*C30)))","v":22.949858837050144},{"$f":"D30-$D$6","v":1.1093434758889735},{"$f":"TAN(E30*PI()/180)/C30","v":3.2099653476528114E-4},{"$f":"ABS(F30)*90/PI()","v":9.1958733401875069E-3},{"$f":"G30^2","v":8.456408648877133E-5},1,{"$f":"H30*I30","v":8.456408648877133E-5}]
[null,2,60.33,22.949092473680864,1.1085771125196935,3.2074814161608018E-4,{"$f":"ABS(F31)*90/PI()","v":9.188757400632918E-3},{"$f":"G31^2","v":8.4433262567686217E-5},2,{"$f":"H31*I31","v":1.6886652513537243E-4}]
[null,3,60.335000000000001,22.948326344793205,1.1078109836320351,3.2049985760526731E-4,9.1816445876628378E-3,{"$f":"G32^2","v":8.4302597334158286E-5},2,{"$f":"H32*I32","v":1.6860519466831657E-4}]
[null,4,60.34,22.947560450325852,1.1070450891646821,3.2025168268778474E-4,9.1745348999864602E-3,{"$f":"G33^2","v":8.4172090631069564E-5},2,{"$f":"H33*I33","v":1.6834418126213913E-4}]
[null,5,60.344999999999999,22.946794790217496,1.1062794290563254,3.2000361681859183E-4,9.1674283363134598E-3,{"$f":"G34^2","v":8.4041742301442973E-5},2,1.6808348460288595E-4]
[null,6,60.35,22.946029364406844,1.1055140032456734,3.1975565995266821E-4,9.1603248953541026E-3,8.3911552188444156E-5,2,1.6782310437688831E-4]
[null,7,60.354999999999997,22.945264172832633,1.1047488116714632,3.1950781204501691E-4,9.153224575819319E-3,8.3781520135382752E-5,2,1.675630402707655E-4]
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[null,17132,145.97999999999999,23.780619744446529,1.9401043832853588,2.3204655983167472E-4,6.64764426444245E-3,4.4191174266574604E-5,2,8.8382348533149209E-5]
[null,17133,145.98500000000001,23.781007236301249,1.9404918751400793,2.3208499212070034E-4,6.6487452684215473E-3,4.4205813644357911E-5,2,8.8411627288715821E-5]
[null,17134,145.99,23.781394745656232,1.9408793844950623,2.3212342389303253E-4,6.6498462575984687E-3,4.4220455249696359E-5,2,8.8440910499392719E-5]
[null,17135,145.995,23.78178227251,1.9412669113488299,2.3216185514855482E-4,6.6509472319698764E-3,4.4235099082447758E-5,2,8.8470198164895516E-5]
[null,17136,146,23.782169816861032,1.9416544556998616,2.3220028588714529E-4,6.6520481915322786E-3,4.4249745142467859E-5,2,8.8499490284935718E-5]
[null,17137,146.005,23.782557378707825,1.9420420175466546,2.3223871610868438E-4,6.6531491362822508E-3,4.4264393429613258E-5,2,8.8528786859226515E-5]
[null,17138,146.01,23.78294495804888,1.9424295968877097,2.3227714581305298E-4,6.6542500662163783E-3,4.4279043943740676E-5,2,8.8558087887481352E-5]
[null,17139,146.01499999999999,23.783332554882698,1.9428171937215275,2.3231557500013185E-4,6.6553509813312471E-3,4.4293696684706796E-5,2,8.8587393369413592E-5]
[null,17140,146.02000000000001,23.783720169207768,1.9432048080465982,2.3235400366980067E-4,6.6564518816234096E-3,4.4308351652367832E-5,2,8.8616703304735664E-5]
[null,17141,146.02500000000001,23.784107801022579,1.9435924398614084,2.3239243182193863E-4,6.6575527670894065E-3,4.4323008846579816E-5,2,8.8646017693159632E-5]
[null,17142,146.03,23.78449545032564,1.9439800891644694,2.3243085945642787E-4,6.6586536377258587E-3,4.4337668267199809E-5,2,8.8675336534399618E-5]
[null,17143,146.035,23.784883117115431,1.9443677559542607,2.3246928657314684E-4,6.6597544935292855E-3,4.4352329914083511E-5,2,8.8704659828167022E-5]
[null,17144,146.04,23.785270801390471,1.9447554402293008,2.325077131719786E-4,6.6608553344963371E-3,4.4366993787088308E-5,2,8.8733987574176617E-5]
[null,17145,146.04499999999999,23.785658503149236,1.9451431419880656,2.3254613925280106E-4,6.6619561606235137E-3,4.4381659886069589E-5,2,8.8763319772139178E-5]
[null,17146,146.05000000000001,23.786046222390251,1.9455308612290807,2.3258456481549815E-4,6.6630569719074934E-3,4.4396328210885058E-5,1,4.4396328210885058E-5]

{"sheet":"STEV A","index":8,"n_rows":43,"n_cols":8,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove (null) radius R01 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'STEVENSON A' CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING LÖFGREN'S AND STEVENSON'S EQUATIONS",null,146.05000000000001]
[]
[null,"OUTPUT","Offset angle β = ",{"$f":"DEGREES(ASIN($D$16))","v":20.823611400323404}," degrees",null,null,"WTE: TAN(TE) per mm"]
[null,"OUTPUT","Overhang d = ",{"$f":"$D$4-SQRT($D$4^2-$D$13)","v":14.592750699395452}," mm","INSTRUCTIONS",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.4806358772086788E-4}]
[null,null,null,null,null,"1. Enter R01 into D2, R2 into D3, L into D4.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",{"$f":"(2*$D$2*$D$13)/($D$2^2+$D$13)","v":79.702762069877295}," mm","2. The optimum offset angle β is shown in D6,",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":22.898512043851916}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":1.0189561087208881E-8}," TAN(TE) per mm2","    and the optimum overhang d is shown in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":84.163097475811895}," mm","3. The %RMS tracking distortion is shown in D26.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":2.0749006435285118}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":-2.1817094409720527E-18}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"($D$2^2*$D$3)/((2*SQRT(2)-2)*$D$2-(2*SQRT(2)-3)*$D$3)","v":7083.4269767230144}," mm2",null,null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.52750746743015997}]
[null,"OUTPUT","(Information only) Radius R1 = ",{"$f":"$D$13/($D$2+$D$15-$D$13/$D$3)","v":54.805742832377405}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":117.42108539946975}," mm",null,null,"Stevenson's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"$D$13/($D$4*$D$9)","v":0.35549217079893952},null,null,null,"Sets the WTE at the inner groove equal to zero"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":88.873042699734881}," mm",null,null,"by placing the inner null radius"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":235.40724930060455}," mm",null,null,"at the inner groove radius."]
[null,"OUTPUT","WTE at R01 =",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":4.6010071472240223E-18}," TAN(TE) per mm",null,null,"The R1 figure calculated is for information only."]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-2.4532844706298999E-4}," TAN(TE) per mm"]
[null,"OUTPUT","WTE at R2 =",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.4806358772086788E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%Tracking Distortion at R01 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":9.7840463010284734E-15},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.52169118808518045},"(Includes RIAA term)"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.52750746743015997},"(Includes RIAA term)"]
[null,"OUTPUT","WTE at Rw + WTE at R2 = ",{"$f":"$D$20+$D$21","v":2.7351406578778894E-6}," TAN(TE) per mm"]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$6,$D$7)*100","v":0.34994377598053911},"(Includes RIAA term)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"STEV A"}]

{"sheet":"PERFECT STEV A","index":9,"n_rows":43,"n_cols":8,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[]
[null,"INPUT","Inner groove (null) radius R01 = ",60.325000000000003," mm",null,null,"QUICK CALCULATOR"]
[null,"INPUT","Outer groove radius R2 = ",146.05000000000001," mm","'PERFECT  STEVENSON A'  CALCULATOR",null,"Enter radius in mm:"]
[null,"INPUT","Tonearm length L = ",250," mm","USING  THE  SOLVER  TOOL",null,146.05000000000001]
[]
[null,"INPUT/OUTPUT","Offset angle β = ",20.845672271827098," degrees","INSTRUCTIONS",null,"WTE: TAN(TE) per mm"]
[null,"INPUT/OUTPUT","Overhang d = ",14.615805936901086," mm","1. Enter R01 into D2, R2 into D3, L into D4.",null,{"$f":"TAN(ASIN(($H$4^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$H$4))-$D$6*PI()/180)/$H$4","v":2.4653007885615697E-4}]
[null,null,null,null,null,"2. Click the orange button to run the Solver.",null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius Rw = ",79.730370688749119," mm","3. The \"perfect\" offset angle β is shown in D6 and",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4)))))","v":22.907757156712638}]
[null,"OUTPUT","Derivative of WTE (Rw) = ",{"$f":"((1/$D$4-($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))^2)/($D$9*SQRT(1-($D$4^2-$D$18^2+$D$9^2)^2/(4*$D$4^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$4^2-$D$18^2+$D$9^2)/(2*$D$4*$D$9)))/$D$9^2","v":-2.2869889575866109E-20}," TAN(TE) per mm2","     the \"perfect\" overhang d is shown in D7.",null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"SQRT($D$13)","v":84.227555973478161}," mm","4. The %RMS tracking distortion is shown in D26.",null,{"$f":"((DEGREES(ASIN((($H$4^2)+(2*$D$4*$D$7)-($D$7^2))/(2*$D$4*$H$4))))-$D$6)","v":2.0620848848855395}]
[null,"OUTPUT","Derivative of TE (Ra) = ",{"$f":"($D$13-$D$4^2+$D$18^2)/(2*$D$4*$D$13)/SQRT(1-($D$13+$D$4^2-$D$18^2)^2/(4*$D$4^2*$D$13))","v":0}," TAN(TE) per mm",null,null,"%Tracking Distortion (includes RIAA term)"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"$D$4^2-$D$18^2","v":7094.2811852653977}," mm2","%RMS Distortion Calculator",null,{"$f":"ABS($H$7)*90/PI()*0.742288880049004*100","v":0.52424645929536029}]
[null,"OUTPUT","(Information only) Radius R1 = ",{"$f":"$D$13/($D$2+$D$15-$D$13/$D$3)","v":54.844908547269064}," mm","1. Enter arm length L in D4, offset angle β in D6 and overhang d in D7."]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$3,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13)))","v":117.60101426051193}," mm","2. Read the resulting %RMS tracking distortion in D26.",null,"Stevenson's Alignment Strategy:"]
[null,"OUTPUT","sin β = ",{"$f":"SIN($D$6*PI()/180)","v":0.3558520285210241},null,null,null,"Sets the WTE at the inner groove radius equal"]
[null,"OUTPUT","Linear offset p = ",{"$f":"$D$4*$D$16","v":88.963007130256031}," mm","SOLVER SETTINGS",null,"to zero by placing the inner null radius"]
[null,"OUTPUT","Mounting distance M = ",{"$f":"$D$4-$D$7","v":235.3841940630989}," mm","Objective Cell =  D19 (WTE at R01)         Equal to Value of: 0",null,"at the inner groove radius."]
[null,"OUTPUT","WTE at R01 = ",{"$f":"TAN(ASIN(($D$2^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$2))-$D$6*PI()/180)/$D$2","v":9.2020142944480445E-19}," TAN(TE) per mm","Changing Cells = D6 (β), D7 (d), D9 (Rw)",null,"The R1 figure calculated is for information only."]
[null,"OUTPUT","WTE at RW = ",{"$f":"TAN(ASIN(($D$9^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$9))-$D$6*PI()/180)/$D$9","v":-2.4653007885615648E-4}," TAN(TE) per mm","Constraints: D10 = 0 (Derivative of WTE function = 0 at Rw)"]
[null,"OUTPUT","WTE at R2 = ",{"$f":"TAN(ASIN(($D$3^2+2*$D$4*$D$7-$D$7^2)/(2*$D$4*$D$3))-$D$6*PI()/180)/$D$3","v":2.4653007885615697E-4}," TAN(TE) per mm","                    D25 = 0 (WTE Rw + WTE R2 = 0)"]
[null,"OUTPUT","%Tracking Distortion at R01 = ",{"$f":"ABS($D$19)*90/PI()*0.742288880049004*100","v":1.9568092602056944E-15},"(Includes RIAA term)","Make Unconstrained Variables Non-Negative."]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"ABS($D$20)*90/PI()*0.742288880049004*100","v":0.52424645929535929},"(Includes RIAA term)","Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"ABS($D$21)*90/PI()*0.742288880049004*100","v":0.52424645929536029},"(Includes RIAA term)","Use Automatic Scaling.     Max Time: 100 seconds."]
[null,"OUTPUT","WTE at Rw + WTE at R2 = ",{"$f":"$D$20+$D$21","v":4.87890977618477E-19}," TAN(TE) per mm","Iterations: 10000.     Convergence: 1E-14     Derivatives: Central."]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"RMS_DISTORTION($D$2,$D$3,$D$4,$D$6,$D$7)*100","v":0.35075181663871491},"(Includes RIAA term)","Require Bounds on Variables."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,{"$f":"RIGHT(CELL(\"filename\",B1),LEN(CELL(\"filename\",B1))-FIND(\"]\",CELL(\"filename\",B1)))","v":"PERFECT STEV A"}]

{"sheet":"LÖF EQN (46)","index":10,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":false,"merged":[[11,8,11,9],[4,3,4,6],[7,8,7,9],[7,5,7,6],[7,1,7,3],[18,5,18,6],[19,5,19,6],[20,5,20,6],[21,5,21,6],[1,3,1,7],[3,3,3,7]]}
[]
[null,null,null,"MEAN AND RMS TRACKING DISTORTION CALCULATOR"]
[]
[null,null,null,"USING LÖFGREN'S EQN (46)"]
[]
[]
[]
[null,"INPUT PARAMETERS",null,null,null,"THE SEVEN TERMS IN EQN (46)",null,null,"WITHOUT RIAA CORRECTION (PER LÖFGREN)"]
[null,"INPUT","Inner radius R1 = ",60.325000000000003," mm","Term 1 =",{"$f":"$D$14^2/($D$15/60*2*PI())^2*(1/($D$10-$D$9))*(1/($D$11^2-(($D$11*SIN($D$12*PI()/180))^2)))","v":1.7818290756341378E-4},null,"MEAN Tracking Distortion = ",{"$f":"$G$9*($G$10-$G$11+$G$12+$G$13-$G$14+$G$15)","v":2.6899521020224392E-5}]
[null,"INPUT","Outer radius R2 = ",146.05000000000001," mm","Term 2 =",{"$f":"($D$10-$D$9)/4","v":21.431250000000002},null,"RMS Tracking Distortion = ",{"$f":"SQRT($J$9)","v":5.186474816310631E-3}]
[null,"INPUT","Arm length L = ",250," mm","Term 3 =",{"$f":"$D$11*SIN($D$12*PI()/180)*LN($D$10/$D$9)","v":82.807013860838552},null,"%RMS Tracking Distortion = ",{"$f":"$J$10*100","v":0.51864748163106311}]
[null,"INPUT","Offset angle β = ",22," degrees","Term 4 =",{"$f":"(2*$D$11*$D$13-$D$13^2)/2*(1/$D$9-1/$D$10)","v":37.67419232778969},null,"WITH RIAA CORRECTION"]
[null,"INPUT","Overhang d = ",16," mm","Term 5 =",{"$f":"($D$11*SIN($D$12*PI()/180))^2*(1/$D$9-1/$D$10)","v":85.337409129628668},null,"%RMS Tracking Distortion = ",{"$f":"$J$11* 0.742288880049004","v":0.3849862582801582}]
[null,"INPUT","Maximum peak recorded velocity V = ",100," mm/sec","Term 6 =",{"$f":"($D$11*SIN($D$12*PI()/180))*(2*$D$11*$D$13-$D$13^2)/2*(1/$D$9^2-1/$D$10^2)","v":82.645187759653041}]
[null,"INPUT","Turntable speed Ω = ",{"$f":"100/3","v":33.333333333333336}," RPM","Term 7 =",{"$f":"(2*$D$11*$D$13-$D$13^2)^2/12*(1/$D$9^3-1/$D$10^3)","v":21.160315939690445}]
[]
[]
[]
[null,null,null,null,null,"This sheet is included for historical purposes and to"]
[null,null,null,null,null,"act as a reference for the distortion calculations"]
[null,null,null,null,null,"based on Löfgren's EQN (46) as described"]
[null,null,null,null,null,"in the writer's tonearm alignment book."]

{"sheet":"TESTS","index":11,"n_rows":202,"n_cols":8,"rows_kept":202,"cut":false,"hidden":false,"merged":[[35,5,35,7],[33,5,33,7],[34,5,34,7],[28,5,28,7],[29,5,29,7],[30,5,30,7],[31,5,31,7],[32,5,32,7],[26,10,26,19],[26,1,26,3],[26,5,26,7],[27,5,27,7],[27,0,27,3],[28,0,28,3],[24,6,24,7],[1,1,1,2],[1,9,1,17],[1,5,1,6],[23,6,23,7],[16,6,16,7],[21,6,21,7],[22,6,22,7],[18,6,18,7],[15,6,15,7],[17,6,17,7],[13,5,13,6],[19,6,19,7],[25,1,25,3],[27,11,27,17]]}
[]
[null,"INPUT PARAMETERS",null,"SETTINGS",null,"PARAMETER SLIDERS",null,"QUICK CALCULATOR"]
[null,"INPUT","Inner groove radius R1 =",{"$f":"($F$3/1000)","v":60.325000000000003}," mm           <<",60325,null,"Enter radius in mm:"]
[null,"INPUT","Outer groove radius R2 = ",{"$f":"$F$4/1000","v":146.05000000000001}," mm           <<",146050,null,146.05000000000001]
[null,"INPUT","Tonearm length L =",{"$f":"$F$5/100","v":250}," mm           <<",25000]
[null,"INPUT","Offset angle β =",{"$f":"$F$6/100","v":21.96}," degrees   <<",2196,null,"WTE: TAN(TE) per mm"]
[null,"INPUT","Overhang d =",{"$f":"$F$7/100","v":16.510000000000002}," mm           <<",1651,null,{"$f":"IFERROR(TAN(ASIN(($H$4^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*$H$4))-$D$6*PI()/180)/$H$4,\"No solution possible\")","v":2.0397917846634022E-4}]
[null,null,null,null,null,null,null,"Tracking Angle (degrees)"]
[null,"OUTPUT","Radius RW = ",85.37096046896815," mm",null,null,{"$f":"IFERROR(((DEGREES(ASIN((($H$4^2)+(2*$D$5*$D$7)-($D$7^2))/(2*$D$5*$H$4))))),\"No solution possible\")","v":23.666402979418823}]
[null,"OUTPUT","Derivative of WTE at Rw = ",{"$f":"IFERROR(((1/$D$5-($D$5^2-$D$18^2+$D$9^2)/(2*$D$5*$D$9^2))*_xlfn.SEC($D$6*PI()/180-ASIN(($D$5^2-$D$18^2+$D$9^2)/(2*$D$5*$D$9)))^2)/($D$9*SQRT(1-($D$5^2-$D$18^2+$D$9^2)^2/(4*$D$5^2*$D$9^2)))+TAN($D$6*PI()/180-ASIN(($D$5^2-$D$18^2+$D$9^2)/(2*$D$5*$D$9)))/$D$9^2,\"No solution possible\")","v":-2.3207110332826991E-15}," TAN(TE) per mm2",null,null,"Tracking Error (degrees)"]
[null,"OUTPUT","Radius Ra = ",{"$f":"IFERROR(SQRT($D$13),\"No solution possible\")","v":89.344389303413976}," mm",null,null,{"$f":"IFERROR(((DEGREES(ASIN((($H$4^2)+(2*$D$5*$D$7)-($D$7^2))/(2*$D$5*$H$4))))-$D$6),\"No solution possible\")","v":1.7064029794188222}]
[null,"OUTPUT","Derivative of TE at Ra = ",{"$f":"IFERROR(($D$13-$D$5^2+$D$18^2)/(2*$D$5*$D$13)/SQRT(1-($D$13+$D$5^2-$D$18^2)^2/(4*$D$5^2*$D$13)),\"No solution possible\")","v":0}," TAN(TE) per mm",null,null,"%Tracking Distortion"]
[null,"OUTPUT","Radius Ra2 = ",{"$f":"IFERROR($D$5^2-$D$18^2,\"No solution possible\")","v":7982.4198999999935}," mm2",null,null,{"$f":"IFERROR(ABS($H$7)*90/PI()*0.742288880049004*100,\"No solution possible\")","v":0.43376192705210986}]
[null,"OUTPUT","Inner null radius R01 = ",{"$f":"IFERROR(IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17-SQRT($D$17^2-$D$13)<$D$3,\"No solution possible\",$D$17-SQRT($D$17^2-$D$13))),\"No solution possible\")","v":65.959398744825009}," mm"]
[null,"OUTPUT","Outer null radius R02 = ",{"$f":"IFERROR(IF($D$17^2-$D$13<0, \"No solution possible\",IF($D$17+SQRT($D$17^2-$D$13)>$D$4,\"No solution possible\",$D$17+SQRT($D$17^2-$D$13))),\"No solution possible\")","v":121.02020412407522}," mm"]
[null,"OUTPUT","sin β = ",{"$f":"IFERROR(SIN($D$6*PI()/180),\"No solution possible\")","v":0.37395920573780045},null,null,"Adjust the five input sliders as required"]
[null,"OUTPUT","Linear offset p = ",{"$f":"IFERROR($D$5*$D$16,\"No solution possible\")","v":93.489801434450115}," mm",null,"to change the parameters."]
[null,"OUTPUT","Mounting distance M = ",{"$f":"IFERROR($D$5-$D$7,\"No solution possible\")","v":233.49}," mm",null,"The data and the plots will update accordingly."]
[null,"OUTPUT","WTE at R1 = ",{"$f":"IFERROR(TAN(ASIN(($D$3^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*$D$3))-$D$6*PI()/180)/$D$3,\"No solution possible\")","v":2.0316835560701805E-4}," TAN(TE) per mm",null,"Distortion figures are based on a"]
[null,"OUTPUT","WTE at RW = ",{"$f":"IFERROR(TAN(ASIN(($D$9^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*$D$9))-$D$6*PI()/180)/$D$9,\"No solution possible\")","v":-2.0406829369490448E-4}," TAN(TE) per mm",null,"1 KHz tone with RIAA de-emphasis applied."]
[null,"OUTPUT","WTE at R2 = ",{"$f":"IFERROR(TAN(ASIN(($D$4^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*$D$4))-$D$6*PI()/180)/$D$4,\"No solution possible\")","v":2.0397917846634022E-4}," TAN(TE) per mm"]
[null,"OUTPUT","%Tracking Distortion at R1 = ",{"$f":"IFERROR(ABS($D$19)*90/PI()*0.742288880049004*100,\"No solution possible\")","v":0.43203771143068298},"(Includes RIAA term)",null,"PLEASE NOTE:"]
[null,"OUTPUT","%Tracking Distortion at RW = ",{"$f":"IFERROR(ABS($D$20)*90/PI()*0.742288880049004*100,\"No solution possible\")","v":0.43395143067479508},"(Includes RIAA term)",null,"Cell H4 (Quick Calculator radius input)"]
[null,"OUTPUT","%Tracking Distortion at R2 = ",{"$f":"IFERROR(ABS($D$21)*90/PI()*0.742288880049004*100,\"No solution possible\")","v":0.43376192705210986},"(Includes RIAA term)",null,"is the only data input cell on this sheet."]
[null,"OUTPUT","%RMS Tracking Distortion = ",{"$f":"IFERROR(RMS_DISTORTION($D$3,$D$4,$D$5,$D$6,$D$7)*100,\"No solution possible\")","v":0.28857320136648795},"(Includes RIAA term)",null,"All other cells are protected."]
[]
[null,null,null,null,null,"SOLVER SETTINGS"]
["EXPERIMENTER'S",null,null,null,null,"Objective Cell: D10 (Derivative of WTE)       Equal to:  Value = 0"]
["TONEARM ALIGNMENT WORKSHOP",null,null,null,null,"Changing Cell: D9 (Rw)"]
[null,null,null,null,null,"Constraints: D9  (Rw) >= D3 (R1)"]
[null,null,null,null,null,"                        D9  (Rw) <= D4 (R2)"]
[null,null,null,null,null,"Make Unconstrained Variables Non-Negative."]
[null,null,null,null,null,"Solving Method: GRG Nonlinear.     Constraint Precision: 1E-14"]
[null,null,null,null,null,"Use Automatic Scaling.     Max Time: 100 seconds."]
[null,null,null,null,null,"Iterations: 10000.     Convergence: 1E-14     Derivatives: Central."]
[null,null,null,null,null,"Require Bounds on Variables."]
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[null,"TAN(ASIN((x^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*x))-$D$6*PI()/180)/x"]
[null,"DEGREES(ASIN((x^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*x)))-$D$6"]
[null,"ABS(TAN(ASIN((x^2+2*$D$5*$D$7-$D$7^2)/(2*$D$5*x))-$D$6*PI()/180)/x)*90/PI()*0.742288880049004"]

{"sheet":"PLOTS","index":12,"n_rows":31,"n_cols":6,"rows_kept":31,"cut":false,"hidden":false,"merged":[[6,1,6,5],[2,1,2,5],[3,1,3,5]]}
[]
[]
[null,"TRACKING DISTORTION AND WTE PLOTS FOR"]
[null,"THE EIGHT ALIGNMENT SHEETS"]
[]
[]
[null,"SELECT THE DESIRED RECORDING PARAMETERS:"]
[]
[null,null,null,"Record speed:","33⅓"," RPM"]
[]
[null,null,null,"Maximum peak recorded velocity:",100," mm / sec"]
[]
[null,null,null,"Equalisation:","RIAA"]
[]
[null,null,null,{"$f":"IF(E13=\"No Eq.\",\"\", \"Frequency:\")","v":"Frequency:"},1000,{"$f":"IF(E13=\"No Eq.\", \"\", \" Hz\")","v":" Hz"}]
[]
[]
[]
[null,"1. Select record speed from drop-down list."]
[null,"2. Enter maximum peak recorded velocity in mm/sec"]
[null,"3. Select equalisation type from drop-down list."]
[null,"4. Enter Frequency in Hz (if requested)."]
[null,"5. The tracking distortion plots are shown in the upper graph."]
[null,"6. The WTE plots are shown in the lower graph."]
[]
[null,"Plots are based on radius R1 = 60.325 mm and radius R2 = 146.05 mm."]
[]
[null,"The plots use the arm length, offset angle and overhang figures"]
[null,"showing on the respective alignment sheets."]
[null,"When data on the alignment sheets is changed, the respective plots"]
[null,"are automatically updated."]

{"sheet":"PLOT DATA","index":13,"n_rows":864,"n_cols":20,"rows_kept":864,"cut":false,"hidden":true,"merged":[[3,13,3,14],[3,15,3,16],[3,1,3,2],[3,3,3,4],[3,5,3,6],[3,7,3,8],[3,9,3,10],[3,11,3,12]]}
["L = ",{"$f":"'LÖF A'!D4","v":250},"mm",{"$f":"'PERFECT LÖF A'!D4","v":250},"mm",{"$f":"'LÖF B'!D4","v":250},"mm",{"$f":"'PERFECT LÖF B'!D4","v":250},"mm",{"$f":"'LÖF C'!D4","v":250},"mm",{"$f":"'PERFECT LÖF C'!D4","v":250},"mm",{"$f":"'STEV A'!D4","v":250},"mm",{"$f":"'PERFECT STEV A'!D4","v":250},"mm"]
["d = ",{"$f":"'LÖF A'!D7","v":16.50182274811911},"mm",{"$f":"'PERFECT LÖF A'!D7","v":16.515729704977336},"mm",{"$f":"'LÖF B'!D7","v":15.635807533403693},"mm",{"$f":"'PERFECT LÖF B'!D7","v":15.630380319935378},"mm",{"$f":"'LÖF C'!D7","v":16.797987974032509},"mm",{"$f":"'PERFECT LÖF C'!D7","v":16.809133710271144},"mm",{"$f":"'STEV A'!D7","v":14.592750699395452},"mm",{"$f":"'PERFECT STEV A'!D7","v":14.615805936901086},"mm"]
["β = ",{"$f":"'LÖF A'!D6","v":21.94887040000955},"degrees",{"$f":"'PERFECT LÖF A'!D6","v":21.962997305126706},"degrees",{"$f":"'LÖF B'!D5","v":21},"degrees",{"$f":"'PERFECT LÖF B'!D5","v":21},"degrees",{"$f":"'LÖF C'!D6","v":21.82842702035023},"degrees",{"$f":"'PERFECT LÖF C'!D6","v":21.840515421669771},"degrees",{"$f":"'STEV A'!D6","v":20.823611400323404},"degrees",{"$f":"'PERFECT STEV A'!D6","v":20.845672271827098},"degrees"]
[null,{"$f":"'LÖF A'!F45","v":"LÖF A"},null,{"$f":"'PERFECT LÖF A'!E43","v":"PERFECT LÖF A"},null,{"$f":"'LÖF B'!E45","v":"LÖF B"},null,{"$f":"'PERFECT LÖF B'!E43","v":"PERFECT LÖF B"},null,{"$f":"'LÖF C'!E45","v":"LÖF C"},null,{"$f":"'PERFECT LÖF C'!E43","v":"PERFECT LÖF C"},null,{"$f":"'STEV A'!E43","v":"STEV A"},null,{"$f":"'PERFECT STEV A'!E43","v":"PERFECT STEV A"},null,null,"DO NOT CHANGE THIS SHEET!"]
["Radius","WTE","Distortion","WTE","Distortion","WTE","Distortion","WTE","Distortion","WTE","Distortion","WTE","Distortion","WTE","Distortion","WTE","Distortion"]
[60.325000000000003,{"$f":"TAN(ASIN(($A6^2+2*B$1*B$2-B$2^2)/2/B$1/$A6)-B$3*PI()/180)/$A6","v":2.0411430801616756E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B6)*$T$12","v":4.3404928017498987E-3},{"$f":"TAN(ASIN(($A6^2+2*D$1*D$2-D$2^2)/2/D$1/$A6)-D$3*PI()/180)/$A6","v":2.0389482974961744E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D6)*$T$12","v":4.3358255942162359E-3},{"$f":"TAN(ASIN(($A6^2+2*F$1*F$2-F$2^2)/2/F$1/$A6)-F$3*PI()/180)/$A6","v":2.3807275359898633E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F6)*$T$12","v":5.0626194867599743E-3},{"$f":"TAN(ASIN(($A6^2+2*H$1*H$2-H$2^2)/2/H$1/$A6)-H$3*PI()/180)/$A6","v":2.3656644643665114E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H6)*$T$12","v":5.0305878498850994E-3},{"$f":"TAN(ASIN(($A6^2+2*J$1*J$2-J$2^2)/2/J$1/$A6)-J$3*PI()/180)/$A6","v":3.2139176997800765E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J6)*$T$12","v":6.8343992035125043E-3},{"$f":"TAN(ASIN(($A6^2+2*L$1*L$2-L$2^2)/2/L$1/$A6)-L$3*PI()/180)/$A6","v":3.2099654833490639E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L6)*$T$12","v":6.8259948113184943E-3},{"$f":"TAN(ASIN(($A6^2+2*N$1*N$2-N$2^2)/2/N$1/$A6)-N$3*PI()/180)/$A6","v":3.6808057177792178E-18},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N6)*$T$12","v":7.8272370408227783E-17},{"$f":"TAN(ASIN(($A6^2+2*P$1*P$2-P$2^2)/2/P$1/$A6)-P$3*PI()/180)/$A6","v":0},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P6)*$T$12","v":0}]
[60.4,{"$f":"TAN(ASIN(($A7^2+2*B$1*B$2-B$2^2)/2/B$1/$A7)-B$3*PI()/180)/$A7","v":2.0065883066122149E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B7)*$T$12","v":4.2670120412313115E-3},2.0043451684475548E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D7)*$T$12","v":4.2622420056803167E-3},2.3489139324957292E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F7)*$T$12","v":4.9949678271060723E-3},2.3338893681297001E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H7)*$T$12","v":4.9630180759524132E-3},{"$f":"TAN(ASIN(($A7^2+2*J$1*J$2-J$2^2)/2/J$1/$A7)-J$3*PI()/180)/$A7","v":3.1768092896372786E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J7)*$T$12","v":6.7554881322237428E-3},{"$f":"TAN(ASIN(($A7^2+2*L$1*L$2-L$2^2)/2/L$1/$A7)-L$3*PI()/180)/$A7","v":3.1728209009591489E-4},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L7)*$T$12","v":6.7470068197100557E-3},{"$f":"TAN(ASIN(($A7^2+2*N$1*N$2-N$2^2)/2/N$1/$A7)-N$3*PI()/180)/$A7","v":-2.5082900140880018E-6},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N7)*$T$12","v":5.3338812240383293E-5},{"$f":"TAN(ASIN(($A7^2+2*P$1*P$2-P$2^2)/2/P$1/$A7)-P$3*PI()/180)/$A7","v":-2.5165732681959621E-6},{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P7)*$T$12","v":5.35149557218477E-5}]
[60.5,1.9608796696813215E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B8)*$T$12","v":4.1698125790747302E-3},1.958572466562246E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D8)*$T$12","v":4.1649063093340865E-3},2.3068359413487907E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F8)*$T$12","v":4.9054889368408605E-3},2.2918624844525066E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H8)*$T$12","v":4.8736478657727383E-3},3.1277106141748638E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J8)*$T$12","v":6.6510797497387761E-3},3.1236743151007238E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L8)*$T$12","v":6.6424965557200458E-3},-5.8228928104177826E-6,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N8)*$T$12","v":1.2382387386080594E-4},-5.8421533349225248E-6,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P8)*$T$12","v":1.2423344910706522E-4}]
[60.6,1.9155843296293198E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B9)*$T$12","v":4.0734919931445391E-3},1.9132135255521153E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D9)*$T$12","v":4.0684504759028123E-3},2.2651437439382438E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F9)*$T$12","v":4.8168304373420005E-3},2.2502211270889773E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H9)*$T$12","v":4.7850974776847176E-3},3.0790420524264039E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J9)*$T$12","v":6.5475860044967816E-3},3.0749582050701549E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L9)*$T$12","v":6.5389016990085851E-3},-9.1037194698869409E-6,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N9)*$T$12","v":1.9359068559301969E-4},-9.1338811693548938E-6,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P9)*$T$12","v":1.9423207443391771E-4},null,"RPM = ",{"$f":"IF(ISNUMBER(PLOTS!E9),PLOTS!E9, 100/3)","v":33.333333333333336}]
[60.7,1.8706988763303643E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B10)*$T$12","v":3.9780430318047165E-3},1.8682649315266409E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D10)*$T$12","v":3.9728672457448877E-3},2.2238341554182416E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F10)*$T$12","v":4.7289855560316146E-3},2.208962113103141E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H10)*$T$12","v":4.6973601431718253E-3},3.0308000761896932E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J10)*$T$12","v":6.4449993937722438E-3},3.0266690396796498E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L10)*$T$12","v":6.4362147405012983E-3},-1.2351053913345436E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N10)*$T$12","v":2.6264528501673904E-4},-1.2392041291499755E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P10)*$T$12","v":2.6351688202319346E-4}]
[60.8,1.8262199318916754E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B11)*$T$12","v":3.8834585119628881E-3},1.8237233028652042E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D11)*$T$12","v":3.8781494278406822E-3},2.1829040209664016E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F11)*$T$12","v":4.6419475841767473E-3},2.1680822895649442E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H11)*$T$12","v":4.6104291575251484E-3},2.982981190576445E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J11)*$T$12","v":6.3433124856817208E-3},2.9788033210850063E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L11)*$T$12","v":6.3344282420289902E-3},-1.5565177375354196E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N11)*$T$12","v":3.3099365258771528E-4},-1.5616915529386994E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P11)*$T$12","v":3.3209386495076725E-4}]
[60.9,1.7821441502984621E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B12)*$T$12","v":3.7897313183152537E-3},1.7795852898617128E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D12)*$T$12","v":3.7842898990368399E-3},2.1423502154547052E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F12)*$T$12","v":4.5557098761895443E-3},2.127578533221503E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H12)*$T$12","v":4.5242978791443043E-3},2.9355819336451588E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J12)*$T$12","v":6.2425179184031525E-3},2.9313575844180039E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L12)*$T$12","v":6.2335348355459274E-3},-1.8746368433559428E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N12)*$T$12","v":3.986417122623817E-4},-1.8808783048499113E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P12)*$T$12","v":3.9996895967341685E-4},null,"Eq. Factor = ",{"$f":"EQUALISATION(2*PLOTS!E15,PLOTS!E13,0)/EQUALISATION(PLOTS!E15,PLOTS!E13,0)","v":0.74228888004900395}]
[61,1.7384682170636296E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B13)*$T$12","v":3.6968544026016901E-3},1.7358475743738032E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D13)*$T$12","v":3.6912816033003062E-3},2.1021696431248145E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F13)*$T$12","v":4.4702658489368021E-3},2.0874477501724403E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H13)*$T$12","v":4.4389597288470471E-3},2.8885988760387314E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J13)*$T$12","v":6.1426083994052258E-3},2.8843283974236726E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L13)*$T$12","v":6.1335272223584786E-3},-2.1894903037683877E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N13)*$T$12","v":4.6559533211435285E-4},-2.1967920380833374E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P13)*$T$12","v":4.6714804664683046E-4}]
[61.1,1.6951888488818748E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B14)*$T$12","v":3.6048207828701857E-3},1.6925068694765823E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D14)*$T$12","v":3.5991175509820076E-3},2.0623592372672508E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F14)*$T$12","v":4.3856089810577455E-3},2.0476868755493657E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H14)*$T$12","v":4.3544081891876783E-3},2.8420286206264956E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J14)*$T$12","v":6.0435767046861794E-3},2.8377123601021126E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L14)*$T$12","v":6.0343981723634593E-3},-2.5011054538165835E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N14)*$T$12","v":5.3186032494343348E-4},-2.5094601453603685E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P14)*$T$12","v":5.3363695093595171E-4}]
[61.2,1.6523027932881555E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B15)*$T$12","v":3.5136235427505763E-3},1.6495599191205211E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D15)*$T$12","v":3.5077908180893634E-3},2.0229159599047337E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F15)*$T$12","v":4.3017328122906496E-3},2.0082928731993542E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H15)*$T$12","v":4.2706368037839669E-3},2.7958678021510115E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J15)*$T$12","v":5.9454156780227021E-3},2.7915061043548122E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L15)*$T$12","v":5.9361405232960136E-3},-2.8095093714431043E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N15)*$T$12","v":5.9744244887682037E-4},-2.8189097617561133E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P15)*$T$12","v":5.9944144281721696E-4}]
[61.3,1.6098068283203936E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B16)*$T$12","v":3.4232558307372781E-3},1.6070034977939729E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D16)*$T$12","v":3.4172945455686306E-3},1.9838368014793952E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F16)*$T$12","v":4.2186309428076975E-3},1.9692627353724065E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H16)*$T$12","v":4.1876391766525285E-3},2.7501130868792052E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J16)*$T$12","v":5.8481182302280773E-3},2.7457062936354958E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L16)*$T$12","v":5.8387471799871476E-3},-3.1147288802815347E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N16)*$T$12","v":6.6234740796287874E-4},-3.125167767500097E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P16)*$T$12","v":6.6456723837412363E-4}]
[61.4,1.5676977621865691E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B17)*$T$12","v":3.333710859481369E-3},1.5648344101897664E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D17)*$T$12","v":3.3276219385959135E-3},1.9451187805441143E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F17)*$T$12","v":4.1362970325586048E-3},1.9305934824129388E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H17)*$T$12","v":4.1054089715527866E-3},2.7047611722579441E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J17)*$T$12","v":5.7516773384197629E-3},2.7003096226054418E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L17)*$T$12","v":5.7422111136307651E-3},-3.4167905524135872E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N17)*$T$12","v":7.2658085275744268E-4},-3.4282607907379317E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P17)*$T$12","v":7.2902000008449972E-4}]
[61.5,1.5259724329359794E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B18)*$T$12","v":3.2449819050915161E-3},1.5230494908759158E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D18)*$T$12","v":3.2387662658769274E-3},1.906758943457519E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F18)*$T$12","v":4.0547248006220383E-3},1.8922821624549021E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H18)*$T$12","v":4.023939911338632E-3},2.6598087865740006E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J18)*$T$12","v":5.6560860452963112E-3},2.6553128167930136E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L18)*$T$12","v":5.6465253610596556E-3},-3.7157207110926645E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N18)*$T$12","v":7.9014838090298142E-4},-3.7282152102604566E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P18)*$T$12","v":7.92805337400856E-4}]
[61.6,1.484627708134588E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B19)*$T$12","v":3.1570623064436074E-3},1.4816456039708315E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D19)*$T$12","v":3.1507208589563354E-3},1.8687543640829454E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F19)*$T$12","v":3.9739080245654555E-3},1.8543258511209999E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H19)*$T$12","v":3.9432257773188203E-3},2.615252688618317E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J19)*$T$12","v":5.5613374584234151E-3},2.6107126322576761E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L19)*$T$12","v":5.5516830240310254E-3},-4.0115454334323518E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N19)*$T$12","v":8.5305553770030759E-4},-4.0250571581996559E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P19)*$T$12","v":8.5592880732367281E-4},null,"No Eq. Flag = ",{"$f":"IF(PLOTS!E13=\"No Eq.\",1,0)","v":0}]
[61.7,1.4436604845444986E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B20)*$T$12","v":3.0699454644991533E-3},1.4406196428222358E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D20)*$T$12","v":3.0634791115349619E-3},1.8311021434909801E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F20)*$T$12","v":3.8938405398125596E-3},1.8167216512253516E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H20)*$T$12","v":3.8632604086246778E-3},2.5710896673544119E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J20)*$T$12","v":5.4674247495287874E-3},2.5665058552580501E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L20)*$T$12","v":5.4576772685206174E-3},-4.3042905530625079E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N20)*$T$12","v":9.1530781667339446E-4},-4.3188125226892157E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P20)*$T$12","v":9.1839591496716824E-4}]
[61.8,1.4030676878073765E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B21)*$T$12","v":2.9836248416320781E-3},1.399968529690233E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D21)*$T$12","v":2.977034478795838E-3},1.7937994096659451E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F21)*$T$12","v":3.8145162390191374E-3},1.7794666924802614E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H21)*$T$12","v":3.7840377015865485E-3},2.5273165415909708E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J21)*$T$12","v":5.3743411538059145E-3},2.5226893019242693E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L21)*$T$12","v":5.364501324025976E-3},-4.5939816627520755E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N21)*$T$12","v":9.76910660127118E-4},-4.609506950493902E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P21)*$T$12","v":9.8021211411843524E-4}]
[61.9,1.3628462721319368E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(B22)*$T$12","v":2.8980939609641694E-3},1.3596892154344793E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(D22)*$T$12","v":2.8913804767389745E-3},1.7568433172158231E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(F22)*$T$12","v":3.7359290714562188E-3},1.7425581312061796E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(H22)*$T$12","v":3.7055516091170251E-3},2.4839301596586949E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(J22)*$T$12","v":5.2820799692268796E-3},2.4792598179343569E-4,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(L22)*$T$12","v":5.2721484828782625E-3},-4.8806441169993447E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(N22)*$T$12","v":1.0378694596980759E-3},-4.8971658496048124E-5,{"$f":"PLOTS!$E$11/($T$9/60*2*PI())*ABS(P22)*$T$12","v":1.0413828077893224E-3}]
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